Lesson 2.05e

2.05e Correlation tests Quiz: OCR Maths, Unit 15

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 2.05e, Correlation tests: 20 multiple choice questions for the OCR Maths (H240), Unit 15: Statistical Hypothesis Testing, written with Revision Ninja.

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The 20 questions

  1. A population is normal with known variance sigma^2 and mean mu. For a sample of size n, what is the distribution of the sample mean X-bar?

    • N(mu/n, sigma^2)
    • N(mu, sigma^2)
    • N(mu, sigma^2/n)
    • N(mu, n sigma^2)

  2. In a test of the mean of a normal distribution with known variance, what test statistic is used?

    • z = (x-bar - mu0)/(sigma/sqrt(n))
    • z = sigma/(x-bar - mu0)
    • z = (x-bar - mu0)/sigma
    • z = (x-bar - mu0) x sqrt(n)

  3. What is the critical value for a two-tailed z-test at the 5% significance level?

    • 1.960
    • 2.576
    • 1.645
    • 2.326

  4. What is the critical value for a one-tailed z-test at the 5% significance level, with the critical region in the upper tail?

    • 2.326
    • 1.960
    • 1.282
    • 1.645

  5. What is the critical value for a two-tailed z-test at the 1% significance level?

    • 2.576
    • 1.645
    • 3.090
    • 2.326

  6. A sample of 16 observations is taken from a normal population with variance 16. What is the standard error of the sample mean?

    • 4
    • 2
    • 16
    • 1

  7. For H0: mu = 20, H1: mu != 20, sigma = 4, n = 16, and sample mean 22, what is z?

    • 1
    • 2
    • 0.5
    • 4

  8. With sigma = 3, n = 9, H0: mu = 100 and H1: mu < 100, a sample mean of 98.5 is found. What is the test statistic?

    • z = -4.5
    • z = 1.5
    • z = -1.5
    • z = -0.5

  9. For a lower one-tailed Z-test at the 5% significance level, what is the critical value?

    • -1.645
    • -1.960
    • -2.326
    • -2.576

  10. With standard deviation sigma = 5 and sample size n = 25, what is the standard error of the mean?

    • 1
    • 25
    • 5
    • 0.2

  11. A test of H0: mu = 20 against H1: mu > 20 has sigma = 4, n = 16 and sample mean 22. What is the p-value to 4 decimal places?

    • 0.0228
    • 0.0455
    • 0.0668
    • 0.9772

  12. The value of Pearson's product-moment correlation coefficient r lies in which range?

    • 0 to 1 only
    • -1 to 1 inclusive
    • -infinity to infinity
    • 0 to 100

  13. In a two-tailed correlation test with critical value 0.6319, what is the outcome for sample correlation r = 0.60?

    • Accept H1
    • Do not reject H0
    • Reject H0
    • Reject H1

  14. For H1: rho > 0 with 5% critical value 0.5494, what is the outcome if sample correlation r = 0.60?

    • Reject H0
    • Test is invalid
    • Do not reject H0
    • Accept H0

  15. What population distribution is assumed when conducting a hypothesis test for Pearson's correlation coefficient?

    • Uniform
    • Binomial
    • Poisson
    • Bivariate normal

  16. For a two-tailed test with critical value 0.4438 and sample correlation 0.40, what is the outcome?

    • Do not reject H0
    • Reject H0
    • Inconclusive
    • Accept H1

  17. What type of relationship between two variables does Pearson's correlation coefficient measure?

    • Causation
    • Non-linear association
    • Exponential growth
    • Linear association

  18. A significant positive sample correlation between two variables indicates what about their relationship?

    • Linear increase together
    • Non-linear decrease
    • Exact linear dependency
    • Direct cause-and-effect

  19. For a correlation test with alternative hypothesis H1: rho > 0, where is the critical region?

    • Distribution centre
    • Upper tail
    • Lower tail
    • Both tails

  20. A researcher wants to test whether the sample mean of a normal population with known variance sigma^2 = 9 and n = 36 differs from mu0 = 50. Which standard error should be used in the test statistic?

    • 3
    • 9
    • 0.5
    • 1.5

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